Massive Multiple-Input Multiple-Output (MIMO) or large-scale MIMO systems were firstly introduced in [1] in which each Base Station (BS) is equipped with dozens to hundreds of antennas to serve tens of users simultaneously through Multi-User MIMO (MU-MIMO) in the same time-frequency resource. Therefore, they can achieve significantly higher spatial multiplexing gains than conventional MU-MIMO systems by linear beamforming methods, e.g., Zero-Forcing (ZF) which can achieve performance very close to the channel capacity, and have drawn great interest from both academia and industry [1]-[3]. Moreover, massive MIMO is viewed as one of the most promising techniques for the 5th Generation (5G) wireless communication systems and has been included in the latest 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) standard release 13 [4], where it is termed as Full Dimension (FD) MIMO.
Despite of the advantages, there still exist very tough challenges for applying massive MIMO to practical systems. To exploit the gains of large-scale antenna arrays, take the downlink as an example, the signals of all the antennas are firstly processed at the baseband, e.g., channel estimation, precoding, etc., then up-converted to the carrier frequency after passing through digital-to-analog (D/A) converters, mixers, and power amplifiers, i.e., Radio Frequency (RF) chains. Outputs of the RF chains are then coupled with the antenna elements. As a result, it introduces huge baseband computation complexity, e.g., O(NtK2), for ZF precoding per precoding unit in the downlink, where Nt and K are the numbers of antennas at the BS and the number of users per MU-MIMO group respectively. Moreover, each antenna element needs a dedicated RF chain, increasing the implementation cost substantially when Nt is very large and requiring high power consumption of mixed signal components, which might result in impractically high complexity for digital baseband precoding. On the other hand, cost-effective variable phase shifters are readily available with current circuit technologies, which enable the possibility to apply high dimensional phase-only RF or analog processing [5], [6]. Due to these reasons, Hybrid Beamforming (HB) [7], [8], was proposed and considered as the promising solution to address this problem in practical systems, e.g., the latest LTE Release 13 [4], in which the global beamforming is decomposed into baseband digital precoding/detection and RF analog precoding/combining respectively so that the signal dimension at the baseband, i.e., the number of RF chains, is reduced to a much smaller number than that of the physical antennas. The analog precoding/combining is also called antenna virtualization [4]. The architecture of the BS transmitter with HB is shown in FIG. 1. Specifically, the K×1 baseband transmitted data vector s 1 is first processed by the first-level digital baseband precoding 2, i.e., xBB=WBBS, where WBB is the NRF×K digital baseband precoding matrix with NRF being the number of RF chains, and xBB is the NRF×1 baseband precoded transmitted symbol vector with xiBB 3, i=1, . . . , NRF, being the ith element in xBB. Then, after xBB is passed through these NRF RF chains 4, a second-level RF analog precoding 5 is applied, i.e., xRF=WRFxBB, where WRF is the Nt×NRF RF analog precoding matrix with θji 6, i=1, . . . , NRF, j=1, . . . , Nt, being the {j,i}th element in WRF, which is generally realized in practice by a phase-shift network consisted of phase shifters 7 and summers 8, and xRF is the Nt×1 transmitted RF symbol vector with xjRF 9, j=1, . . . , Nt, being the jth element in xRF. Finally, xRF is transmitted by the Nt antennas 10. Similarly, the architecture of the BS receiver with HB is shown in FIG. 2. Specifically, let the Nt×1 RF symbol vector received by the Nt antennas and after the Bandpass Filters (BPF) and Low-Noise Amplifiers (LNA) 11, be yRF with yjRF 12, j=1, . . . , Nt, being the jth element in yRF. First, yRF is processed by the first-level RF analog combining 13, i.e., yBB=WRF,TyRF, where WRF is the Nt×NRF RF analog combing matrix as in FIG. 1 and yBB is the NRF×1 baseband symbol vector received by the NRF RF chains with yiBB 14, i=1, . . . , NRF, being the ith element in yBB. Then, the digital baseband detection 15 is applied, i.e., ŝ=GBByBB, where GBB is the K×NRF digital baseband detection matrix, and ŝ 16 is the K×1 baseband detected symbol vector. Other than the conventional micro-wave commercial communication systems, HB also has been considered as the most promising beamforming method for millimeter Wave (mm-Wave) communication systems with large-scale antenna arrays [7], [8].
The prior three HB methods were proposed in [9]-[11] for the downlink transmission. In [9], the beam space or mask of the channel vector of each user is computed first based on full CSI, i.e., several vectors in the Discrete Fourier Transformation (DFT) matrix. The analog precoding matrix of a MU-MIMO group is consisted of the beam spaces of all the K users. In [10], an iterative HB method for Single-User MIMO (SU-MIMO) with partial CSI is derived. In [11], the phase component of the MU-MIMO channel matrix is used as the analog precoding matrix. However, all of these methods face at least one of the two following problems:    1) The full CSI, i.e., the channel coefficient of each antenna, is assumed to be available at the baseband to compute the analog precoding matrix, which is impractical for practical systems with limited number of RF chains. If the CSI is measured by users transmitting uplink Sounding Reference Signals (SRSs), however, due to the limited number of RF chains in HB systems, the full CSI is unavailable. If the CSI is measured by downlink CSI-RS, the pilot overhead is substantially huge because of the large number of antennas. Moreover, the measured CSI has to be quantized before feeding back to the BS. Hence, full CSI is unavailable for practical systems.    2) The analog precoding matrix is derived based on the CSI of users in a single MU-MIMO group. However, for practical OFDM-based systems, e.g., LTE/LTE-A, as multiple MU-MIMO groups are scheduled in one OFDM symbol, these algorithms suffer large performance loss as they are only suited for a single MU-MIMO group.
For these reasons, this patent provides HB methods and apparatus designed to overcome these shortcomings of prior arts. The proposed methods construct a subspace for each user firstly based on the principal angle information contained in the partial CSI. Then, the unified analog beamforming matrix is derived with the subspaces of all the users in the system. Finally, the base band beamforming is employed.